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Fuzzy transforms in image compression and fusion

Irina Perfilieva (2007)

Acta Mathematica Universitatis Ostraviensis

An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of F -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.

Gelfand transform for a Boehmian space of analytic functions

V. Karunakaran, R. Angeline Chella Rajathi (2011)

Annales Polonici Mathematici

Let H ( ) denote the usual commutative Banach algebra of bounded analytic functions on the open unit disc of the finite complex plane, under Hadamard product of power series. We construct a Boehmian space which includes the Banach algebra A where A is the commutative Banach algebra with unit containing H ( ) . The Gelfand transform theory is extended to this setup along with the usual classical properties. The image is also a Boehmian space which includes the Banach algebra C(Δ) of continuous functions on...

Generalized Fractional Evolution Equation

Da Silva, J. L., Erraoui, M., Ouerdiane, H. (2007)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic...

Generalized functions on adeles. Linear and non-linear theories

Yakov V. Radyno, Yauhen M. Radyna (2010)

Banach Center Publications

We consider various generalizations of linear homogeneous distributions on adeles and construct a number of algebras of non-linear generalized functions on adeles and totally disconnected groups such as the discrete adeles.

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